Predicting when a complex system — such as a climate network, an economy, or even the human heart — is on the verge of abrupt collapse has long been one of science’s most difficult challenges. These so-called critical transitions — sudden shifts between stable states of a system, such as from a healthy ecosystem to a collapsed one — can trigger rapid and irreversible changes, from ecological collapses to epileptic seizures, without clear warning. A new study led by Dr. Zhiqin Ma and Professor Chunhua Zeng from Kunming University of Science and Technology, in collaboration with Professor Yi-Cheng Zhang from North University of China and Dr. Thomas Bury from McGill University, introduces a breakthrough approach using machine learning to detect early signs of such transitions. Their work, published in Communications Physics, outlines a system-specific method that learns from historical data to predict tipping points more accurately than previous universal models.
Critical transitions are ubiquitous — whether in the sudden bleaching of coral reefs, financial market crashes, or the onset of cardiac arrhythmia. Previous prediction methods relied on generic signals such as increasing variance, meaning the measure of how much data fluctuates over time, or lag-one autocorrelation, which measures how similar a system is to its own recent past. Both come from dynamical systems theory, the study of how systems evolve over time. However, these indicators have often failed when applied to real-world noisy datasets. As Dr. Ma explained, “Generic early warning signals can fail to signal a transition if the time series is too short, too noisy, or too non-stationary, or if the transition corresponds not to a local bifurcation, but a global bifurcation, or no bifurcation at all.” A bifurcation refers to a sudden change in a system’s behavior, like a river abruptly splitting into two branches when conditions change. To overcome these limitations, the team trained machine learning models on surrogate data — artificially generated datasets that statistically resemble real ones — allowing the models to learn unique, system-specific behaviors without relying on restrictive theoretical assumptions.
Dr. Ma and her colleagues developed a new framework called Surrogate Data-based Machine Learning, which generates vast quantities of training data by replicating statistical patterns found in historical events. Their approach was tested across diverse real-world examples, including oxygen-depleted ocean sediments, ancient human societies, and biological heart rhythms. When compared with traditional indicators like variance and autocorrelation, Surrogate Data-based Machine Learning consistently demonstrated higher sensitivity, meaning it could accurately detect true warnings, and greater specificity, allowing it to avoid false alarms. In simpler terms, it detected genuine signals while minimizing mistakes.
The models were tested using different types of machine learning systems, including convolutional neural networks, which identify spatial and time-based patterns; long short-term memory networks, which recognize long-range connections in data; and support vector machines, which separate information into distinct categories by finding the best dividing boundaries. These algorithms achieved remarkable performance scores — a combined statistical measure of both precision and accuracy — that were close to perfection in several cases.
The team analyzed real-world examples of rapid transitions. In sediment cores from the Mediterranean Sea, they detected recurring episodes where oxygen levels plummeted — events historically linked to marine anoxia, the total loss of oxygen in ocean water that can lead to mass extinctions. The Surrogate Data-based Machine Learning model trained on earlier transitions successfully anticipated later ones. Similarly, when applied to ice-core records from Antarctica, the approach predicted abrupt temperature shifts that ended glacial periods. It also detected cultural tipping points in pre-Hispanic Pueblo societies, where construction activity data revealed that societal collapses were preceded by critical slowing down, meaning a gradual loss of resilience and a longer recovery time from small disturbances before complete collapse.
The performance evaluation revealed that Surrogate Data-based Machine Learning outperformed standard techniques in most cases, particularly in scenarios where transitions did not follow classical bifurcation models. As Dr. Ma noted, “Our method is not bound by the restricting assumption of a local bifurcation like previous methods. By learning directly from data of past transitions, it adapts to the real-world system it’s predicting.” The study further demonstrated that the Surrogate Data-based Machine Learning classifiers maintained robustness across multiple surrogate generation techniques, including amplitude-adjusted Fourier transforms, which are mathematical methods that create new data while maintaining both the overall variability and structure of the original time series. The team also used iterative algorithms that preserve complex properties in time-based data to enhance accuracy.
Beyond environmental and biological systems, this method could transform risk forecasting in economics, energy networks, and public health. Many catastrophic events, such as financial crashes or grid blackouts, emerge from intertwined dynamics that defy simple mathematical models. By identifying warning signs in system-specific data, Surrogate Data-based Machine Learning could provide crucial lead time to mitigate or prevent collapse. “Machine learning classifiers trained on rich surrogate data of past transitions could be crucial in advancing our ability to prepare for or avert critical transitions,” said Dr. Ma, emphasizing that the approach complements rather than replaces existing early-warning tools.
Dr. Ma and her team emphasized that future developments will focus on refining how the models interpret varying distances from a transition, turning classification into a more continuous and dynamic measure of risk. They believe that as more high-quality time-series data becomes available — long-term measurements collected at regular intervals — the Surrogate Data-based Machine Learning framework will continue to evolve, providing a powerful and unified way to understand stability and resilience across systems ranging from natural ecosystems to global economies.
This innovative convergence of historical data modeling and artificial intelligence marks a major step toward anticipating the unpredictable. By training on the echoes of past crises, Surrogate Data-based Machine Learning opens a pathway to foresee — and perhaps forestall — the next major tipping point in nature or society.
Journal Reference
Ma Zhiqin, Zeng Chunhua, Zhang Yi-Cheng, and Bury Thomas M. “Predicting critical transitions with machine learning trained on surrogates of historical data.” Communications Physics (2025). DOI: https://doi.org/10.1038/s42005-025-02172-4
About the Authors
Dr. Zhiqin Ma holds a bachelor’s degree in Physics and a PhD in Systems Science from Kunming University of Science and Technology, Kunming, China. His research focuses on statistical physics and complex systems, the detection and analysis of early warning signals, and the application of machine learning in complex systems. Dr. Ma takes an interdisciplinary approach, combining physics, mathematics, and computer science to reveal the universal laws underlying the dynamic evolution of systems near tipping points. His research findings have been published in several journals, including Communications Physics, Physical Review Research, and Europhysics Letters.
Professor Chunhua Zeng primarily engaged in research on statistical physics and complex systems. He has published over 120 SCI papers in journals such as Natil. Sci. Rev., Comm. Phys., Phys. Rev. B, Phys. Rev. Research, and Phys. Rev. E.
Dr. Yi-Cheng Zhang is a Senior Professor of Physics at the University of Fribourg, Switzerland, and a member of the Academia Europaea. He received a PhD from Sissa Trieste and La Sapienza University. His research spans big data, artificial intelligence, complex networks, information economy, cyber-physical systems, statistical physics, complexity science, and finance. He is widely recognized for seminal contributions, including co-developing the Kardar-Parisi-Zhang (KPZ) equation — for which his supervisor, Giorgio Parisi, was awarded the Nobel Prize in Physics in 2021 — and introducing the Minority Game model in econophysics. His recent work focuses on the theoretical foundations of next-generation AI assistants. He has published over 250 academic papers in international journals, including Proceedings of the National Academy of Sciences (PNAS), Physics Reports, and Physical Review Letters, as well as more than 31,000 citations in total.
Dr. Thomas Bury does research at the intersection of machine learning and nonlinear dynamics. He is interested in developing early warning signals for tipping points for a broad range of complex systems. He holds a PhD from the University of Waterloo in applied mathematics and has published his work in journals such as PNAS and Nature Communications.
